Yes it does, I just tried it. I also bought my copy from Steam and the trainer 1.2 worked just fine until yesterday. The GPF fault started coming up, so I tried registering the trainer & Steam to no avail, as well as turning the GPF all the way down. Just downloaded the 1.2.1 trainer & it works fine, so I turned the GPF back up and all is fine, even with a 1.2 trainer save game. OH and I almost forgot, MAJOR PROPS to Caliber for getting the trainer up so quickly!
Well the new trainer with the new patch crashes the game for me. I get a general protection fault as shown in the Link.
I am using the no-cd exe supplied by RZR in the rzr-bl21 release. The game works fine with the update and no-cd but crashes as soon as the trainer is enabled either 'F1' 'load' crash or 'load' then 'F1' key, crash.